Optical fiber span with low differential mode delay

ABSTRACT

A fiber span comprising: a first optical fiber and a second optical fiber coupled to the first optical fiber, both fibers comprising the an inner core region with maximum refractive index delta, Δ 0 ≦0.1% and an outer radius R 1 &gt;4.5 μm, an outer core region with an outer radius R 2  and a minimum refractive index delta Δ 1  and alpha value α≧5, wherein Δ 1 &lt;Δ 0 , 5.5 μm≦R 2 −R 1 ≦12 μm; a cladding including a low index ring surrounding the core and a minimum refractive index delta Δ R,MIN &lt;Δ 1 ; and an outer cladding having Δ Outer-Clad &gt;Δ R,MIN ; the first fiber introducing differential mode delay DMD 1  for wavelengths between 1525 and 1570 nm such that |DMD 1 |≦100 ps/km, and a first differential mode delay slope DMDS 1 ; the second fiber introducing differential mode delay DMD 2  for wavelengths between 1525 and 1570 nm such that |DMD 2 |≦100 ps/km, and a second differential mode delay slope DMDS 2  that has an opposite sign from the first dispersion slope DMDS 1 ; wherein total differential mode delay provided by the first fiber in conjunction with the second fiber is DMD tot =DMD 1 +DMD 2 , and −1.0 ps/km&lt;DMD tot &lt;1.0 for all wavelengths between 1525 nm and 1570 nm.

This application claims the benefit of priority under 35 U.S.C. §119 ofU.S. Provisional Application Ser. No. 62/288,843 filed on Jan. 29, 2016,the content of which is relied upon and incorporated herein by referencein its entirety.

BACKGROUND

The disclosure relates generally to optical fiber spans comprisingoptical fiber pairs and more specifically to optical fiber spanscomprising optical fiber pairs for low DMD applications.

The explosive growth in the volume and variety of multi-mediatelecommunication applications continues to drive speed demands forinternet traffic and motivate research in long-haul fiber-optictelecommunication.

Modern high-data-rate coherent transmission systems are alreadyapproaching information capacity limits. To exploit the full capacity inoptical fiber, advanced multi-level modulation formats, such as QAM,and/or superchannel or OFDM systems will be needed. However thesesystems require higher signal-to-noise ratios (SNR) than are currentlyfeasible. Fiber nonlinearities and fiber attenuation are the keyperformance limitations that prevent the higher SNRs from beingachieved.

Compared to ordinary single-mode fibers, large effective area fibers aredesirable because they can carry more optical power before the onset ofnonlinear propagation impairments. However, to achieve extremely largeeffective areas (Aeff>>140 μm²) with low bend loss, these largeeffective area fibers are often multimoded. Thus, they typically canintroduce modal dispersion into the fiber spans. Modal dispersion is thespreading of pulses due to the different velocities of the modes. Insuch fibers, the light propagates in many different modes within in thefiber core. A “mode” is an allowable path for the light to travelthrough the fiber core. A multimode fiber allows many light propagationpaths within its core, while a single-mode fiber allows only one lightpath. In a multimode fiber, the time it takes for light to travelthrough the fiber core is different for each mode, resulting in aspreading of the pulse at the output of the fiber. The difference in thetime delay between modes is the called Differential Mode Delay (MID).Modal dispersion limits the bandwidth of optical fiber spans, limitingfiber span's information carrying capacity, i.e., how far a transmissionsystem can operate at a specified bit error rate. Typically, as thefiber's effective area increases, deleterious nonlinear distortionsdecrease, but the number of supported modes, and hence the modaldispersion increases, making it difficult to achieve the desired systemperformance.

One solution is to utilize only large effective area fibers that haveessentially no DMD over a wide wavelength range, but such fiber designswould be difficult and expensive to make in practice, and if such fibersare made they would have be made to very tight manufacturing tolerances.

No admission is made that any reference cited herein constitutes priorart. Applicant expressly reserves the right to challenge the accuracyand pertinence of any cited documents.

SUMMARY

Some of the embodiments of the disclosure relate to fiber spancomprising

-   -   (I) a first optical fiber, the first optical fiber comprising a        core having        -   (i) an inner core region with maximum refractive index            delta, Δ₀≦0.1% and an outer radius R₁ wherein R₁>4.5 μm, and        -   (ii) an outer core region with an outer radius R₂ and a            minimum refractive index delta Δ₁ and alpha value α wherein            α≧5, wherein Δ₁<Δ₀, 5.5 μm≦R₂−R₁≦12 μm; and            -   an annular cladding surrounding the core, the cladding                including        -   (i) a low index ring surrounding the core and having a            minimum refractive index delta Δ_(RMIN), where Δ_(R,MIN)<Δ₁;            and        -   (ii) an outer cladding with a refractive index delta            Δ_(Outer-Clad) relative to pure silica, such that            Δ_(Outer-Clad)>Δ_(R,MIN);        -   said first fiber introducing differential mode delay DMD₁            for wavelengths between 1525 and 1570 nm, and a first            differential mode delay slope DMDS₁; and    -   (II) a second optical fiber coupled to the first optical fiber,        the second optical fiber comprising a core having:        -   (i) an inner core region with maximum refractive index delta            of the core, Δ₀≦0.1% wherein R₁>4.5 μm, and        -   (ii) an outer core region with an outer radius R₂ and a            minimum refractive index delta Δ₁ and alpha value α wherein            α≧5, where Δ₁<Δ₀, and 5.5 μm≦R₂−R₁≦12 μm; and            -   an annular cladding surrounding the core, the cladding                including        -   (i) a low index ring surrounding the core and having a            minimum refractive index delta Δ_(RMIN), where Δ_(R,MIN)<Δ₁;            and        -   (ii) an outer cladding with a refractive index delta            Δ_(Outer-Clad) relative to pure silica, such that            Δ_(Outer-Clad)>Δ_(R,MIN); said second fiber introducing            differential mode delay DMD₂ for wavelengths between 1525 nm            and 1570 nm, and a second differential mode delay slope            DMDS₂ that has an opposite sign from the first dispersion            slope DMDS₁;    -   and wherein    -   total differential mode delay provided by said first fiber in        combination with said second fiber is DMD_(tot)=DMD₁+DMD₂, and        DMD_(tot) is less than 1.0 ps/km and more than −1.0 ps/km for        all wavelengths between 1525 nm and 1570 nm.

Some of the embodiments of the disclosure relate to fiber spancomprising:

-   -   (I) a first optical fiber, the first optical fiber comprising a        core having        -   (i) an inner core region with maximum refractive index            delta, Δ₀≦0.1% and an outer radius R₁ wherein R₁>4.5 μm, and        -   (ii) an outer core region with an outer radius R₂ and a            minimum refractive index delta Δ₁ and alpha value α wherein            α≧5, wherein Δ₁<Δ₀, 5.5 μm≦R₂−R₁≦12 μm; and            -   an annular cladding surrounding the core, the cladding                including        -   (i) a low index ring surrounding the core and having a            minimum refractive index delta Δ_(RMIN), where Δ_(R,MIN)<Δ₁;            and        -   (ii) an outer cladding with a refractive index delta            Δ_(Outer-Clad) relative to pure silica, such that            Δ_(Outer-Clad)>Δ_(R,MIN);        -   the first fiber introducing differential mode delay DMD₁ for            wavelengths between 1525 and 1570 nm such that 1            ps/km≦|DMD₁|≦100 ps/km, and a first differential mode delay            slope DMDS₁; and    -   (II) a second optical fiber coupled to the first optical fiber,        the second optical fiber comprising a core having:        -   (i) an inner core region with maximum refractive index delta            of the core, Δ₀≦0.1% wherein R₁>4.5 μm, and        -   (ii) an outer core region with an outer radius R₂ and a            minimum refractive index delta Δ₁ and alpha value α wherein            α≧5, where Δ₁<Δ₀, and 5.5 μm≦R₂−R₁≦12 μm; and            -   an annular cladding surrounding the core, the cladding                including        -   (i) a low index ring surrounding the core and having a            minimum refractive index delta Δ_(RMIN), where Δ_(R,MIN)<Δ₁;            and        -   (ii) an outer cladding with a refractive index delta            Δ_(Outer-Clad) relative to pure silica, such that            Δ_(Outer-Clad)>Δ_(R,MIN); the second fiber introducing            differential mode delay DMD₂ for wavelengths between 1525            and 1570 nm such that 1 ps/km≦|DMD₂|≦100 ps/km, and a second            differential mode delay slope DMDS₂ that has an opposite            sign from the first dispersion slope DMDS₁;    -   and wherein    -   total differential mode delay provided by the first fiber in        combination with the second fiber is DMD_(tot)=DMD₁+DMD₂, and        DMD_(tot) is less than 1.0 ps/km and more than −1.0 ps/km for        all wavelengths between 1525 nm and 1570 nm.

Some of the embodiments of the disclosure relate to fiber spancomprising:

-   -   (I) a first optical fiber, the first optical fiber comprising a        core having:        -   (i) an inner core region with a maximum refractive index            delta Δ₀≦0.1%, and an outer radius R₁ wherein R₁>4.5 μm, and        -   (ii) an outer core region with an outer radius R₂ and a            minimum refractive index delta Δ₁ and alpha value α wherein            α≧5, wherein Δ₁<Δ₀, 5.5 μm≦R₂−R₁≦12 μm; and            -   an annular cladding surrounding the core, the cladding                including        -   (i) a low index ring surrounding the core and having a            minimum refractive index delta Δ_(RMIN), where Δ_(R,MIN)<Δ₁;            and        -   (ii) an outer cladding with a refractive index delta            Δ_(Outer-Clad) relative to pure silica, such that            Δ_(Outer-Clad)>Δ_(R,MIN);        -   the first fiber introducing positive differential mode delay            DMD₁ for all wavelengths between 1525 and 1570 nm such that            1 ps/km≦DMD₁≦100 ps/km, and a first differential mode delay            slope DMDS₁; and    -   (II) a second optical fiber coupled to the first optical fiber,        the second optical fiber comprising    -   a core having:        -   (i) an inner core region with maximum refractive index delta            of the core, Δ₀≦0.1% wherein R₁>4.5 μm, and        -   (ii) an outer core region with a minimum refractive index            delta Δ₁, where Δ₁<Δ₀, 5.5 μm≦R₂−R₁≦12 μm, and alpha value            α≧5; and    -   an annular cladding surrounding the core, the cladding        including:        -   (i) a low index ring surrounding the core and having a            minimum refractive index delta Δ_(RMIN), where Δ_(R,MIN)<Δ₁;            and        -   (ii) an outer cladding with a refractive index delta            Δ_(Outer-Clad), such that Δ_(Outer-Clad)>Δ_(R,MIN); the            second fiber introducing negative differential mode delay            DMD₂ for all wavelengths between 1525 and 1570 nm wherein            −100 ps/km≦DMD₂≦−1 ps/km, and a second differential mode            delay slope DMDS₂ that has an opposite sign from the first            dispersion slope DMDS₁;    -   and wherein        -   total differential mode delay DMD_(tot)=DMD₁+DMD₂ provided            by the first fiber in combination with the second fiber is            DMD_(tot)=DMD₁+DMD₂ and DMD_(tot) is less than 1.0 ps/km and            more than −1.0 ps/km for all wavelengths between 1525 and            1570 nm.

Some of the embodiments of the disclosure relate to fiber spancomprising:

-   -   (I) a first optical fiber, the first optical fiber comprising a        core having:        -   (i) an inner core region with a maximum refractive index            delta Δ₀≦0.1%, and an outer radius R₁ wherein R₁>4.5 μm, and        -   (ii) an outer core region with an outer radius R₂ and a            minimum refractive index delta Δ₁ and alpha value α wherein            α≧5, wherein Δ₁<Δ₀, 5.5 μm≦R₂−R₁≦12 μm; and            -   an annular cladding surrounding the core, the cladding                including        -   (i) a low index ring surrounding the core and having a            minimum refractive index delta Δ_(RMIN), where Δ_(R,MIN)<Δ₁;            and        -   (ii) an outer cladding with a refractive index delta            Δ_(Outer-Clad) relative to pure silica, such that            Δ_(Outer-Clad)>Δ_(R,MIN);        -   the first fiber introducing negative differential mode delay            DMD₁ for all wavelengths between 1525 and 1570 nm such that            −100 ps/km≦DMD₁≦−1 ps/km, and a first differential mode            delay slope DMDS₁; and    -   (II) a second optical fiber coupled to the first optical fiber,        the second optical fiber comprising    -   a core having:        -   (i) an inner core region with maximum refractive index delta            of the core, Δ₀≦0.1% wherein R₁>4.5 μm, and    -   (ii) an outer core region with a minimum refractive index delta        Δ₁, where Δ₁<Δ₀, 5.5 μm≦R₂−R₁≦12 μm, and alpha value α≧5; and an        annular cladding surrounding the core, the cladding including:

(i) a low index ring surrounding the core and having a minimumrefractive index delta Δ_(RMIN), where Δ_(R,MIN)<Δ₁; and

(ii) an outer cladding with a refractive index delta Δ_(Outer-Clad),such that Δ_(Outer-Clad)>Δ_(R,MIN), the second fiber introducingpositive differential mode delay DMD₂ for all wavelengths between 1525and 1570 nm wherein 1 ps/km≦DMD₂≦100 ps/km, and a second differentialmode delay slope DMDS₂ that has an opposite sign from the firstdispersion slope DMDS₁;

-   -   and wherein        -   total differential mode delay DMD_(tot)=DMD₁+DMD₂ provided            by the first fiber in combination with the second fiber is            DMD_(tot)=DMD₁+DMD₂ and DMD_(tot) is less than 1.0 ps/km and            more than −1.0 ps/km for all wavelengths between 1525 and            1570 nm.

According to some embodiments the core is a Ge-free core. According tosome embodiments the core comprises silica doped with chlorine (Cl).According to at least some of the embodiments, both the first and thesecond fibers have few-moded cores.

According to some embodiments the inner core region of the first opticalfiber has the outer radius R₁>5 μm (e.g., between 5 and 12 μm); and (ii)the inner core region of the second optical fiber has the outer radiusR₁>5 μm (e.g., between 5 and 12 μm). According to some embodiments theinner core region of the first optical fiber has the outer radius R₁>6am; and (ii) the inner core region of the second optical fiber also hasthe outer radius R₁>6 am. According to some embodiments the inner coreregion of the first optical fiber has the outer radius R₁>7 μm; and (ii)the inner core region of the second optical fiber has the outer radiusR₁>7 μm. According to some embodiments R₁≦10 μm (e.g. 7 μm≦R₁≦9 μm) inboth the first and the second optical fibers. According to someembodiments the first optical fiber has 6 μm≦R₂−R₁≦11 μm; and the secondoptical fiber also has 6 μm≦R₂−R₁≦11 μm. According to some embodimentsthe first optical fiber has 8 μm≦R₂−R₁≦10 μm; and the second opticalfiber also has 8 μm≦R₂−R₁≦10 μm.

According to some embodiments the first optical fiber has the ratio ofR₂/R₁<2.2, and the second optical fiber also has the ratio of R₂/R₁<2.2.

According to some embodiments the first fiber has a length L₁ and thesecond fiber has a length L₂ and wherein 10 km≦L₁+L₂≦120 km, for example40 km≦L₁+L₂≦100 km.

In some embodiments the optical fiber and first the second optical fiberhave fiber cores that are Ge-free silica based core and the fiber coreshave step index profiles, the cores of each optical fiber having alphavalue is greater than or equal to 5. In some embodiments the core'salpha value (α) is ≧6, for example ≧8, for example α≧10, or α≧12. Insome embodiments each of the cores has alpha values between 6 and 100,for example between 6 and 25.

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from the description or recognized by practicing theembodiments as described in the written description and claims hereof,as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description are merely exemplary, and areintended to provide an overview or framework to understand the natureand character of the claims.

The accompanying drawings are included to provide a furtherunderstanding, and are incorporated in and constitute a part of thisspecification. The drawings illustrate one or more embodiment(s), andtogether with the description serve to explain principles and operationof the various embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates schematically some exemplary embodiments of fiberspans;

FIG. 2 is a schematic cross-sectional view of one embodiment of anoptical fiber that can be utilized in the fiber span of FIG. 1;

FIG. 3 illustrates schematically the refractive index delta profile ofthe exemplary optical fiber embodiment of FIG. 2;

FIG. 4 is a plot of DMD vs. wavelength for the optical fibers of thefirst optical fiber span embodiment, as well as for the entire fiberspan;

FIG. 5 is a plot of DMD vs. wavelength for the optical fibers of thesecond optical fiber span embodiment, as well as for the entire secondfiber span;

FIG. 6 is a plot of DMD vs. wavelength for the optical fibers of thethird optical fiber span embodiment, as well as for the entire thirdfiber span; and

FIG. 7 is a plot of DMD vs. wavelength for the optical fibers of theforth optical fiber span embodiment, as well as DMD of the entire fourthfiber span.

DETAILED DESCRIPTION

Reference will now be made in detail to embodiments of optical fibersfor use as long haul transmission fibers, examples of which areillustrated in the accompanying drawings. Whenever possible, the samereference numerals are used throughout the drawings to refer to the sameor like parts.

Terminology

The following terminology will be used herein to describe the opticalfibers, with some of the parameters being introduced and defined belowin connection with the various example embodiments:

The term “refractive index profile,” as used herein, is the relationshipbetween the refractive index or the relative refractive index and theradius of the fiber.

The term “relative refractive index,” also referred to as “refractiveindex delta”, “relative refractive index delta” or as to “index delta”,as used herein, is defined as:

Δ(r)=[n(r)² −n _(REF) ²)]/2n _(REF) ²,

where n(r) is the refractive index at radius r, unless otherwisespecified. The relative refractive index is defined at 1550 nm unlessotherwise specified. The reference index n_(REF) is pure silica glass,the relative refractive index is represented by 4 and its values aregiven in units of “%”, unless otherwise specified. In cases where therefractive index of a region is less than the reference index n_(REF),the relative index percent is negative and is referred to as having adepressed region or depressed-index, and the minimum relative refractiveindex is calculated at the point at which the relative index is mostnegative unless otherwise specified. In cases where the refractive indexof a region is greater than the reference index n_(REF), the relativeindex percent is positive and the region can be said to be raised or tohave a positive index.

The term “downdopant,” as used herein, is a dopant which has apropensity to lower the refractive index of glass relative to pure,undoped SiO₂. A downdopant may be present in a region of an opticalfiber having a positive relative refractive index when accompanied byone or more other dopants which are not downdopants. Likewise, one ormore other dopants which are not downdopants may be present in a regionof an optical fiber having a negative relative refractive index.

As used herein, the term “differential mode delay” or DMD (ps/km) isdefined herein as group delay difference between the LP₀₁ and LP₁₁optical modes. As used herein, DMD=delay₀₁−delay₁₁, wherein delay₀₁ isthe time it takes for the light in LP01 mode to propagate through 1 kmof fiber length; and delay₁₁ is the time it takes for the light in LP11mode to propagate through the same 1 km of fiber length.

As used herein, the “effective area” A_(eff) of an optical fiber is thearea of the optical fiber in which light is propagated and is definedas:

${A_{eff} = {2\pi \frac{\left( {\int_{0}^{\infty}{E^{2}{rdr}}} \right)^{2}\ }{\int_{0}^{\infty}{E^{4}{rdr}}}}},$

where E is the electric field associated with light propagated in thefiber and r is the radius of the fiber. In the examples describedherein. The effective area at the signal wavelength, of Aeff,s isdetermined at a wavelength of 1550 nm, unless otherwise specified.

The cutoff wavelength of a mode is the maximum wavelength at which amode can propagate in the optical fiber. The cutoff wavelength of asingle mode fiber is the minimum wavelength at which an optical fiberwill support only one propagating mode. The cutoff wavelength of asingle mode fiber corresponds to the highest cutoff wavelength among thehigher order modes. Typically the highest cutoff wavelength correspondsto the cutoff wavelength of the LP₁₁ mode. A mathematical definition ofa theoretical cutoff wavelength is given in Single Mode Fiber Optics,Jeunhomme, pp. 39 44, Marcel Dekker, New York, 1990, wherein thetheoretical fiber cutoff is described as the wavelength at which themode propagation constant becomes equal to the plane wave propagationconstant in the outer cladding.

As used herein, the term “few moded fiber” refers to a fiber supportingthe propagation of more than a single mode fiber but fewer modes than anormal multimode fiber (i.e., not greater than 20 LP modes). The numberof propagating modes and their characteristics in a cylindricallysymmetric optical fiber with an arbitrary refractive index profile isobtained by solving the scalar wave equation (see for example T. A.Lenahan, “Calculation of modes in an optical fiber using a finiteelement method and EISPACK,” Bell Syst. Tech. J., vol. 62, no. 1, p.2663, Feb. 1983).

The bend resistance or bend performance of an optical fiber may bemeasured by the induced attenuation of light propagating through thefiber under prescribed test conditions. The bend performance of theoptical fibers described herein is determined using the pin array bendtest to compare the relative resistance of the optical fibers tobending. To perform this test, attenuation is measured for an opticalfiber with essentially no induced bending loss. The optical fiber isthen woven about the pin array and the attenuation is once againmeasured. The loss induced by bending, typically expressed in units ofdB, is the difference between the two attenuation measurements. The pinarray is a set of ten cylindrical pins arranged in a single row and heldin a fixed vertical position on a flat surface. The pin spacing is 5 mm,center to center. The pin diameter is 0.67 mm. The optical fiber iscaused to pass on opposite sides of adjacent pins. During testing, theoptical fiber is placed under a tension sufficient to make the opticalfiber conform to the portion of the periphery of the pins contacted bythe fiber. The test pertains to macro-bend resistance of the opticalfiber.

The term “α-profile” or “alpha profile,” as used herein, refers to arelative refractive index profile, expressed in terms of Δ which is inunits of “%”, where r is the radius and which follows the equation,

${\Delta = {\Delta_{0}\left\lbrack {1 - \left( \frac{r}{R_{1}} \right)^{\alpha}} \right\rbrack}},$

where Δ₀ is the maximum relative refractive index, R₁ is the radius ofthe core, r is in the range r_(i)≦r≦r_(f), Δ is as defined above, r_(i)is the initial point of the α-profile, r_(f) is the final point of theα-profile, and α is a real number exponent. As defined herein, for agraded index profile, the alpha value is less than 1.8<α<2.3, and a stepindex profile has an alpha value that is at least 5. The fiberembodiments described herein have step index profiles with α>5, forexample α>6, or α>8, or even α≧10. The alpha value may be, for example,6≦α≦100.

Unless otherwise specified herein, the above-referenced properties ofthe optical fiber disclosed herein and discussed below are measured ormodeled at a signal wavelength of 1550 nm.

As shown in FIG. 1, the embodiments of fiber spans 5 disclosed hereincomprise at least two different fibers 10, 10′. According to at leastsome embodiments optical fibers are few moded optical fibers 10′. A spanlength is a distance between a receiver R and a transmitter T, or ifoptical amplifiers are used, the distance between two consecutiveoptical amplifiers A1 and A2. Preferably, according to the embodimentsdescribed herein the span length of an optical transmission system is 10to 130 km, and in some embodiments 40 km to 120 km, for example about 50km, 60 km, 75 km, 80 km, 100 km or therebetween. One of the opticalfibers (e.g., optical fiber 10) causes differential mode delay (DMD) ofan opposite sign but of about the same magnitude to that caused by theother optical fiber (e.g., optical fiber 10′), thus the DMD introducedby the first fiber 10 is compensated by the DMD introduced by the secondfiber 10′. (As used herein, the term DMD when applied to an opticalfiber refers to the group delay difference between the LP₀₁ and LP₁₁modes in that fiber, because as these are the only two modes (modefamilies) intended to support propagation—i.e., these two modes can beused as information-carrying channels in fibers 10, 10′. Other opticalmodes, if exist, will be lossy, and are not utilized in the embodimentsdescribed herein.)

DMD₁ may be positive, and DMD₂ negative, i.e., in such embodiments 1ps/km≦DMD₂≦100 ps/km and −100 ps/km≦DMD₂≦−1 ps/km for all wavelengthsbetween 1525 and 1570 nm. Also, for example, DMD₁ may be negative, andDMD₂ positive, i.e., in such embodiments −100 ps/km≦DMD₂≦−1 ps/km and 1ps/km≦DMD₂≦100 ps/km for all wavelengths between 1525 and 1570 nm.

For example, if the optical fiber 10 introduces differential mode delayDMD₁ into the fiber span, where DMD₁ is 1 ps/km≦DMD₁≦100 ps/km for allwavelengths between 1525 and 1570 nm, then the second fiber10′introduces differential mode delay DMD₂ such that −100 ps/km≦DMD₂−1ps/km, and such that |DMD₁|≈|DMD₂|

throughout the wavelength band of interest. Thus, the optical fiber span5 has a total differential mode delay differential mode delay DMD_(tot),where DMD_(tot)=DMD₁+DMD₂, such that |DMD_(tot)|≦1 ps/km, and preferably≦0.5 ps/km for all wavelengths within the specified wavelength band. Forexample, in at least some embodiments −0.5 ps/km≦DMD_(tot)≦0.5 for allwavelengths between 1525 nm and 1570 nm. Similarly, for example, if theoptical fiber 10 introduces a negative differential mode delay DMD₁ intothe fiber span, where DMD₁ is −100 ps/km≦DMD₁≦−1 ps/km for allwavelengths between 1525 and 1570 nm, then the second fiber 10′introduces positive differential mode delay DMD₂ such that 1ps/km≦DMD₂≦100 ps/km, and such that |DMD₁|≈|DMD₂| throughout thewavelength band of interest and such that |DMD_(tot)|≦1 ps/km.Preferably 0.9 DMD₁≦|DMD₂|≦1.1 DMD₁. In some embodiments 0.95DMD₁≦|DMD₂|≦1.05 DMD₁, and in some embodiments 0.97 DMD₁≦DMD₂≦1.03DMD₁.We discovered that the practical difficulties associated with achievinggood DMD cancellation increase with the increase in DMD of theconstituent optical fibers forming the fiber pair of the span 5, becausethe manufacturing and deployment tolerances needed to achieve sufficientcancellation becomes very stringent. Consequently, the span length andthe whole system reach are reduced. For this reason, in order to operateover longer fiber lengths, we designed our fibers such that each fiber10, 10′ has a DMD below 100 ps/km (in absolute value). In addition, werealized that if each fiber 10, 10′ in the fiber pair has a DMD below100 ps/km (in absolute value), it can enable longer span length and thelength of each fiber used within the span, and this also minimizes thetransmission losses due to fiber splicing. For example, as shown in FIG.1, and described above, the embodiments of fiber spans 5 disclosedherein comprise two different fibers 10, 10′ (also referred to herein asa fiber pair). In at least some embodiments, the first fiber 10, has alength L₁ and the second fiber 10′ has a length L₂ and 10 km≦L₁+L₂≦120km (e.g., 10 km≦L₁+L₂≦100 km, or 50 km≦L₁+L₂≦120 km, or 40 km≦L₁+L₂≦100km, or 50 km≦L₁+L₂≦100 km) and in some embodiments 80 km≦L₁+L₂≦120 km,or 80 km≦L₁+L₂≦100 km. In the exemplary embodiments described herein,0.9≦L₁/L₂≦1.15, 0.9≦L₁/L₂≦1.15, for example 0.95≦L₁/L₂≦1.1. In someembodiments the total length L_(TOT) of the fiber span is between 50 kmand 120 km, and each fiber has a length of at least 10 km, preferably atleast 22.5 km, Preferably each span utilizes no more than two fibers perspan—i.e., each span comprises only two fiber 10, 10′. In some exemplaryembodiments 0.95 DMD₁≦DMD₂≦1.05 DMD₁, and the absolute value of DMDslope (ps/nm/km) at the operating wavelength (e.g., 1550 nm) of theoptical fiber 10 is within 5% of that of the optical fiber 10′ (but thetwo slopes have opposite signs). In some exemplary embodiments 0.97DMD₁≦|DMD₂|≦1.03 DMD₁, and, the absolute value of DMD slope (ps/nm/km)at the operating wavelength (e.g., 1550 nm) of the optical fiber 10 iswithin 5% of that of the optical fiber 10′ and 0.95≦L₁/L₂≦1.1.Preferably, as shown in FIG. 1 the fiber span 5 has no more than two DMDcompensating fibers (i.e., only 1 optical fiber 10 and only one opticalfiber 10′).

In some embodiments, for ease of deployment, the optical fiber 10 iscomprised of shorter segments of fiber 10 that are spliced togetherduring cabling or deployment in the field. These segments of fiber 10are substantially identical to one another (i.e., the segments of theoptical fiber 10 have essentially the same effective area, and the samesign for DMD). Similarly, for ease of deployment, the optical fiber 10′may be comprised of shorter segments of fiber that are spliced togetherduring cabling or deployment in the field, and the spliced segments offiber 10′ are substantially identical to one another (i.e., the segmentsof the optical fiber 10′ have essentially the same effective area (atthe same wavelength) and the same sign for DMD).

In some embodiments −1 ps/km≦DMD_(tot)≦1 ps/km for all wavelengthsbetween 1525 nm and 1570 nm. In some embodiments −0.8ps/km≦DMD_(tot)≦0.8 ps/km for all wavelengths between 1525 nm and 1570nm. In some embodiments −0.5 ps/km≦DMD_(tot)≦0.5 ps/km, or even −0.25ps/km≦DMD_(tot)≦0.25 ps/km for all wavelengths between 1525 nm and 1570nm, and in some embodiments −0.15 ps/km≦DMD_(tot)≦0.15 ps/km for allwavelengths between 1525 nm and 1570 nm. According to at least someembodiments DMD_(tot) is positive for at least some of the wavelengthsin the 1525 nm and 1570 nm range and is negative for at least some ofwavelengths in the 1525 nm and 1570 nm range. According to at least someembodiments DMD_(tot)=0 ps/km at least one wavelength situated between1540 nm and 1560 nm. The plot of DMD_(tot) vs. wavelength may beapproximately linear or approximately parabolic, so that it may crossthe zero value at one or more points within the wavelengths of interest(i.e., there are one or two points where the plot of DMD_(tot) crossesthe horizontal axis and DMD_(tot) is zero). According to at least someof the exemplary embodiments, DMD_(tot)=0 ps/km at least a wavelengthsituated between 1540 nm and 1560 nm.

In the embodiments described herein, one fiber has DMD that has apositive slope (i.e., its DMD increases as the wavelength increases),and the other fiber has a DMD that has a negative slope (i.e., its DMDdecreases as the wavelength increases). For example if the optical fiber10 has a positive DMD slope (i.e., DMDS₁>0), then optical fiber 10′ hasa negative DMD slope (i.e., DMDS₂<0). Similarly if the optical fiber 10has a negative DMD slope (DMDS₁<0), then optical fiber 10′ has apositive DMD slope (i.e., DMDS₂>0).

FIG. 2 is a cross sectional view of optical fiber (“fiber”) 10, 10′according to the embodiments described herein. The various exampleembodiments of fiber 10, 10′ are now described below with respect tocross-sectional view of the fiber and plots of the correspondingrefractive index profile(s). FIG. 3 illustrates schematically therefractive index profile(s) of FIG. 2 fibers 10 and 10′. As can be seenfrom FIGS. 2 and 3, the fiber embodiments 10, 10′ have a step-index core20. The core 20 includes a central, inner core region 21 and an annularouter core region 22 that is adjacent to and directly surrounds theinner core region. The inner core region 21 has higher refractive indexthan the outer core region 22. The parameters (refractive index deltasand radii) of the inner core region and the outer core region are chosensuch that the differential mode delay introduced by one fiber (e.g.,fiber 10′) compensates for the differential mode delay introduced by theother fiber (e.g., fiber 10). Preferably, fiber embodiments 10, 10′ havea maximum refractive index delta of the core, Δ₀ in % measured relativeto pure SiO₂ is −0.02%≦Δ₀≦0.1%, and fiber cores 20 are Ge-free whichhelps the fibers to have very low attenuation.

According to some exemplary embodiments the optical fiber 10, 10′comprises: (I) a Ge-free silica based core 20 having

-   -   (i) an inner core region 21 with the maximum refractive index        delta Δ₀ wherein −0.02%≦Δ₀≦0.1%; a radius R₁>4.5 μm (e.g., R₁≧5        μm, R₁≧6 μm, or R₁≧7 μm), and    -   (ii) an outer core region 22 with an radius R₂, and the        refractive index delta Δ₁, where Δ₀>Δ₁, and −0.05≦Δ₁<0, and        alpha value α wherein α≧5 (for example, 12 or 15, or 20, or 25,        or therebetween; such that the fiber has an effective area        Aeff,s of LP₀₁ mode such that at a wavelength λs, 140        μm²<Aeff<325 μm²    -   where λs is situated in the wavelength range of 1555 nm to 1545        nm (e.g., =1550 nm); and        (II) an annular cladding 50 surrounding the core 20, the        cladding 50 comprising    -   (i) a low index ring 53 surrounding the core and having a        minimum refractive index delta Δ_(RMIN), wherein and        Δ_(R,MIN)<Δ₁ and (b) Δ_(R,MIN)≦−0.30% measured relative to pure        SiO₂ (e.g., Δ_(R,MIN)≦−0.35%, or −0.4%≦Δ_(R,MIN)≦−0.30%, or        −0.4%≦Δ_(R,MIN)≦−0.33%); and    -   (ii) an outer cladding 54 surrounding the low index ring 53, the        outer cladding 54 having a refractive index delta Δ_(Outer-Clad)        relative to pure silica, such that Δ_(Outer-Clad)>Δ_(R,MIN); and        the difference between the relative refractive index of the core        Δ₀.        Note: the first optical fiber 10 and the second optical fiber        10′ are not single mode fibers.

Preferably, the core 20 of fibers 10 and 10′ is a segmented core (withtwo segments 21, 22) with a step refractive index profile (i.e., core 20is not a graded index core), and according to at least some embodiments,5.5 μm≦R₂−R₁≦12 μm. In some embodiments the difference between radii R₂and R₁ in the optical fiber 10 and/or 10′ is 6 μm≦R₂−R₁≦11 μm. In someembodiments 7 μm≦R₂−R₁≦11 μm, or 7 μm≦R₂−R₁≦10 μm. In some embodiments 8μm≦R₂−R₁≦10 μm or even 8 μm≦R₂−R₁≦9.5 μm. In some embodiments R₂ isabout 10 μm to 25 μm. In some embodiments 12 μm≦R₂≦20 μm, for example,13 μm, 14 μm, 15 μm, 16 μm, 17 μm, 18 μm, 19 μm, or therebetween. Forexample, in some embodiments R₂ is 15 μm≦R₂18 μm.

Various embodiments will be further clarified by the following examples.

Tables 1A and 1B, below, provide parameters for four exemplary fiberspans comprising eight different fiber embodiments (fiber examples 1-8).

The optical fiber embodiments 10, 10′ depicted in Tables 1A-1B and shownschematically in FIGS. 2 and 3 each comprise a Ge-free silica based core20, a cladding 50, and at least one coating 60 (not shown) surroundingthe glass cladding 50. In these embodiments the core index profiles arestep index profiles with α>10, and as described above each of the cores20 includes an inner core region 21 and an outer core region 22. Theouter core region 22 has a lower refractive index than that of the innercore region. The outer radius of the inner core region 21 is R₁.Preferably, in both fibers 10 and 10′ R₁>4.5 μm, to help provide theabsolute value of DMD at or below 100 ps/km, and even more preferablyR₁≧5 μm and ≦12 μm. The outer radius of the outer core region 20 is R₂.Thus, the outer radius of the core 20 is also R₂. Each of the claddings50 in fibers 10,10′ includes a moat (a low refractive index ring, alsoreferred to herein as a low index ring)) 53, and outer cladding 54. Theouter radius of the cladding 50 is R_(outer). In the exemplaryembodiments described herein R_(outer)=62.5 μm. In alternativeembodiments R_(outer) may be different, for example between 62.5 μm and125 μm.

Preferably, according to at least some embodiments, the relativerefractive index profile of the optical fibers 10, 10′ are structured toprovide attenuation of less than 0.18 dB/km (e.g., 0.155 dB/km to 0.178dB/km) at the 1550 nm wavelength. For example, in some embodiments theattenuation is not greater than 0.168 dB/km, e.g., 0.155 dB/km to 0.168dB/km) at the 1550 nm wavelength.

The central core region 21 may be pure silica, or silica doped with Cl,and has an index of refraction that is approximately that of puresilica. The relative refractive index (also referred to herein asrefractive index delta) of the core region 21 is, for example,−0.02%≦Δ₀≦0.1%; relative to pure silica. In some embodiments the radiusR₁ for each of the fibers 10 and 10′ is about 4.5 μm to 12 μm, e.g., 4.5μm to 10 μm or 5 μm to 12 μm, or 5.5 μm to 12 μm. In some embodiments,for example, the radius R₁ for both fibers 10 and 10′ is in the range of4.5 μm and 9.5 μm, or 5.5 μm to 9.5 μm, or 6 μm to 9.5 μm. In someembodiments at least one of the fibers (10 or 10′) has the inner coreradius R₁ that is greater than 6 μm, more preferably greater 7 μm, forexample greater 8 μm, or greater 8.5 m. In some embodiments, forexample, the radius R₁ for each of the fibers 10 and 10′ within thefiber span 5 is in the range of 7 μm and 9.5 μm.

In at least some exemplary embodiments both fibers 10, 10′ in the fiberpair forming a fiber span 5 have a ratio of R₂/R₁≦2.2, for exampleR₂/R₁≦2, and in some embodiments both fibers in the fiber pair n have aratio of R₂/R₁≦2.19. In at least some embodiments both fibers in thefiber span (i.e., both fiber 10 and fiber 10′) have the ratio ofR₂/R₁≦2.17. This helps to keep DMD contributions of both fibers to orbelow 100 ps/km.

According to at least some embodiments the R₁ value of the optical fiber10 does not equal to the R₁ value of the optical fiber 10′ (i.e., theouter radii of the inner cores are dis-similar.) According to at leastsome embodiments the difference in R₁ values of optical fibers 10 and10′ is at least 1 μm (e.g., 1 μm to 2.25 μm, or 1 μm to 1.5 μm). Forexample, according to some embodiments the difference in R₁ values ofoptical fibers 10 and 10′ is at least 1.25 μm, and in some embodimentsabout 1.3 μm, i.e., in these exemplary embodiments R₁ value of theoptical fiber 10 is not equal to the R₁ value of the optical fiber 10′.According to at least some embodiments the difference in radii R₁between optical fibers 10 and 10′ is 1.2 μm to 2 μm, for example 1.25 μmto 1.5 μm.

As described above, the core 20 is surrounded by the cladding 50. Atleast a portion of the cladding 50 (e.g., the low index ring 53) isdown-doped relative to the core 20 (and relative to pure silica), andcontains fluorine (F) or boron (B) as a downdopant. In the exemplaryembodiments described herein, the downdopant is F1. The core 20 may alsoinclude chlorine (e.g. <0.05 wt %), or some alkali, for examplepotassium (e.g., <0.05 wt %, or 20 to 1000 ppm by weight) to control itsviscosity.

The low index ring 53 (also referred to as a moat herein) of thecladding 50 has a relative refractive index delta (Δ_(R,MIN)) and anouter radius R₃ and is directly adjacent to the core 20. As describedherein, a moat is a low refractive index cladding region situatedbetween a core and an outer cladding region, and is the lowestrefractive index portion of the cladding. The low index ring (moat) 53can be made of glass doped with an index decreasing dopant such as F, orB. In the embodiments of Tables 1A, 1B the low index ring 53 comprisessilica doped with F. The outer cladding layer 54 has an outer radiusR_(outer) and a higher maximum index of refraction than that of the lowindex ring 53, the outer cladding surrounds and is in directly contactwith the low index ring 53. Preferably Δ₀>Δ_(cladMAX)>Δ_(R,MIN), whereis the Δ_(cladMAX) is maximum refractive index delta of the cladding 50.In the exemplary embodiments of FIG. 3, Δ₀>Δ₁>Δ_(R,MIN) andΔ_(Outer-Clad)>Δ_(R,MIN). In the exemplary embodiment of FIG. 3 therelative refractive index delta (Δ_(outer-clad)) of the outer cladding54 is −0.275%, but it can be higher or lower than −0.275%. In theembodiment of FIG. 3 the core alpha is at least 5, for example 6≦α≦50.For example, in fiber embodiments of Tables 1A, 1B the value of thecore's alpha parameter is at least 10 (α≧10.)

Table 1A and 1B illustrate the properties of four embodiments ofexemplary fiber spans, each comprising of optical fiber pairs 10 and10′. Table 1A provides refractive index deltas and the outer radii foreach fiber region, while Table 1B discloses the effective areas of thefibers at the signal wavelength of 1550 nm, the performance of eachfiber, and the performance of four fiber span that include matched fiberpairs 10, 10′. In the embodiments of Tables 1A, 1B the absolute value ofDMD of each fiber 10, 10′ is <75 ps/km, for example 30≦|DMD₁|≦75 ps/km,and 30≦|DMD₂|≦75 ps/km.

TABLE 1A outer core Inner region ring Fiber's Refractive index core coreradial ring radius Fiber deltas (%) radius radius width radius widthspan fiber Δ₀; Δ₁; Δ_(R,MIN); Δ_(Outer-Clad) R₁ R₂ (R₂ − R₁) Δ₀ − Δ₁R₂/R₁ R₃ R₃ − R₂ 1 1 0.08; −0.037; −0.37; −0.275 8.47 17.73 9.26 0.1172.09 32.73 15.00 2 0.08; −0.004; −0.37; −0.275 7.19 15.44 8.25 0.0842.15 30.44 15.00 2 3 0.08; −0.005; −0.37; −0.275 7.14 15.63 8.49 0.0852.19 30.63 15.00 4 0.08; −0.039; −0.37; −0.275 8.56 17.61 9.05 0.1192.06 32.61 15.00 3 5 0.08; −0.037; −0.37; −0.275 8.48 17.72 9.24 0.122.09 32.72 15.00 6 0.08; −0.004; −0.37; −0.275 7.19 15.47 8.28 0.08 2.1530.47 15.00 4 7 0.08; −0.005; −0.37; −0.275 7.15 15.6 8.47 0.09 2.1830.62 15.00 8 0.08; −0.039; −0.37; −0.275 8.55 17.62 9.07 0.12 2.0632.62 15.00

TABLE 1B Slope LP01 Fiber's effective DMD (ps/nm/km) pin array LP02Fiber area Aeff (μm²) (ps/km) at (dB)* at cutoff LP11 cutoff span fiberat 1550 nm at 1550 nm 1550 nm 1550 nm (μm) (μm) 1 1 258 50.0 1.0 0.252.05 3.00 2 258 −50.0 −1.0 0.29 2.17 3.15 2 3 258 50.0 −1.0 0.3 2.053.00 4 258 −50.1 1.0 0.24 2.17 3.15 3 5 315 40.2 0.966 0.27 2.55 3.69 6188 −39.8 −1.009 0.78 1.55 2.27 4 7 146 41.3 −0.908 2.61 1.223 1.77 8262 −40.2 0.97 0.3 2.17 3.15

It is noted that although the fibers 10 and 10′ in each of the fiberspan of Table 1A have identical Δ₀ value, this is not necessary. Otherembodiments the two fibers 10 and 10′ in the fiber pair do not have tohave matched (identical) Δ₀ values. It is also noted that most of theoptical fibers 10, 10′ of Table 1A, 1B may support additional modes inthe C band besides the LP01 and LP11, such as the LP02 and LP21 modes.However, these additional modes are predicted to have very largeeffective areas (600 μm² to 800 μm², or larger), low effective index,and very high loss, and thus cannot support transmission over the longdistances and are ignored herein for the purposes of DMD calculation.

The relative refractive index delta of the outer cladding 54 of theoptical fibers 10, 10′ of Table 1A, 1B can be changed to influence modecutoffs without significantly impacting the effective areas. (Note: thecutoffs wavelengths of for the fibers can be easily modified by changingΔ_(Outer-Clad) As the Δ_(Outer-Clad) increases, the cutoff wavelengthdecreases. The more negative is the value of Δ_(Outer-Clad), the largeris the cutoff wavelength. The pin array bend loss value is also impactedby outer cladding's delta.)

FIGS. 4-7 depict the modeled performance of fiber spans 1, 2, 3, and 4respectively. They provide the DMD contributed by each fiber vs.wavelength, as well as the residual differential group delay (DMD_(tot))vs. wavelength associated with each optical fiber pair 10, 10′. Forexample, FIG. 4 corresponds to the optical fiber span #1. This figureshows that the optical fiber 10 (fiber #1 in Tables 1A,1B) has DMD thatis positive in value, and that DMD of the fiber increases from a minimumvalue of about 25 ps/km (at 1525 nm) to a maximum value of about 65ps/km-70 ps/km (at 1570 nm). Thus, the differential mode delay slope(also referred to herein as DMD slope herein) of the optical fiber 10corresponding to exemplary optical fiber #1 is positive (i.e., in thisembodiment DMDS₁ is positive). FIG. 4 also depicts that the opticalfiber 10′ (fiber #2 in Table 1A, 1B) has negative DMD slope, and thatDMD decreases from a minimum value of about 27 ps/km at the 1525 nmwavelength to about −72 ps/km at the 1570 nm wavelength. Thus, the DMDslope of optical fiber 10′ (i.e., in this embodiment DMDS₂)corresponding to the exemplary optical fiber #2 is negative. That is,DMD slopes of fiber 10′ and 10 have opposite signs. FIG. 4 alsoillustrates residual deferential mode delay (DMD_(tot)) of the fiberspan #1 that comprises fibers #1 and #2. As seen in FIG. 4, the residualdeferential mode delay of the optical fiber span #1 depicted in Tables1A, 1B increases from about 0.125 ps/km (at 1525 nm) to about 0.5 ps/km(at 1540 nm) and then decreases to about −0.8 ps/km (at 1570 nm) i.e.,in this embodiment −0.8 ps/km≦DMD_(tot)≦0.8 ps/km, thus this embodimentsatisfies the requirement −1 ps/km≦DMD_(tot)≦1 ps/km over the entireC-band wavelength range (1525 nm-1570 nm). The residual differentialmode delay of the optical fiber span #1 is zero (DMD_(tot)=0) at awavelength of about 1557 nm.

FIG. 5 corresponds to the optical fiber span #2. This figure shows thatthe optical fiber 10 (fiber #3 in Tables 1A,1B) has DMD that is positivein value, and that DMD of fiber #3 decreases from a maximum value ofabout 75 ps/km at a 1525 nm wavelength to less than 30 ps/km at 1570 nmwavelength. Thus, the DMD slope of the optical fiber 10 corresponding toexemplary optical fiber #3 is negative. FIG. 5 also depicts that theoptical fiber 10′ (fiber #4 in Table 1A,1B) has negative DMD, and thatDMD changes from a minimum value of about −80 ps/km to about at 1525 nmwavelength to about −30 ps/km at the 1570 nm wavelength. Thus, the DMDslope of optical fiber 10′ corresponding to the exemplary optical fiber#4 is positive. That is, DMD slopes of fiber 10′ and 10 have oppositesigns. FIG. 5 also illustrates residual deferential mode delay(DMD_(tot)) of the fiber span #2 that comprises fibers #3 and #4. Asseen in FIG. 5, the residual deferential mode delay of the optical fiberspan #2 depicted in Tables 1A, 1B varies between about −0.125 ps/km (at1525 nm) wavelength and about 0.14 ps/km (at 1570 nm) i.e., in thisembodiment −0.15 ps/km≦DMD_(tot)≦0.15 ps/km over the entire C-band range(1525 nm-1570 nm wavelength range). The residual differential mode delayof the optical fiber span #1 is zero at a wavelength of about 1553 nm.

FIG. 6 corresponds to the optical fiber span #3. This figure shows thatthe optical fiber 10 (fiber #5 in Tables 1A,1B) has DMD that ispositive, and that increases from a maximum value of about 15 ps/km at1525 nm wavelength to about 60 ps/km at 1570 nm wavelength. Thus, theDMD slope of the optical fiber 10 that corresponds to the exemplaryfiber 5 is positive. FIG. 6 also depicts that the optical fiber 10′(fiber 6 in Table 1A,1B) has DMD that is negative in value, and that itchanges from about −15 ps/km at about 1525 nm wavelength to about −60ps/km at 1570 nm wavelength. That is, the DMD slope of the optical fiber10 (exemplary fiber #6) of this embodiment negative. Thus DMD slopes ofoptical fiber 10 and optical fiber 10′ have the opposite signs. FIG. 6also illustrates residual deferential mode delay (DMD_(tot))) of thefiber span #3 that comprises fibers #1 and #2. As seen in FIG. 6, theresidual deferential mode delay of the optical fiber span #3 depicted inTables 1A, 1B is −0.5 ps/km≦_(tot) DMD≦0.75 ps/km over the entire C-bandrange (1525 nm-1570 nm wavelength range). The residual differential modedelay of the optical fiber span #1 is zero at a wavelength of about 1558nm.

FIG. 7 corresponds to the optical fiber span #4. This figure shows thatthe optical fiber 10 (fiber #7 in Tables 1A,1B) has DMD that is positivein value, and that DMD of the fiber decreases about 65 ps/km (at 1525nm) to about 25 ps/km (at 1570 nm). Thus, the DMD slope of the opticalfiber 10 corresponding to exemplary fiber 7 is negative. FIG. 7 alsodepicts that the optical fiber 10′ (fiber #8 in Table 1A,1B) hasnegative DMD, and that DMD changes from about −65 ps/km at the 1525 nmwavelength to about −20 ps/km at the 1570 nm wavelength. That is, theDMD slope of optical fiber 10′ corresponding to the exemplary fiber 8 ispositive. Thus, DMD slopes of fiber 10′ and 10 have opposite signs. FIG.7 also illustrates residual deferential mode delay (DMD_(tot)) of thefiber span #4 that comprises fibers #7 and #8. As seen in FIG. 7, theresidual deferential mode delay of the optical fiber span #4 depicted inTables 1A, 1B changes from about −0.65 ps/km (at 1525 nm) to about 1ps/km at 1570 nm—i.e., this embodiment satisfies the requirement −1ps/km≦DMD_(tot)≦1 ps/km over the entire C-band wavelength range (1525nm-1570 nm). The residual differential mode delay of the optical fiberspan #4 is zero (DMD_(tot)=0) at a wavelength of about 1543 nm.

Thus, according to some embodiments a fiber span 5 comprises:

-   -   (I) a first optical fiber 10, the first optical fiber 10        comprising a core 20 having        -   (i) an inner core region 21 with maximum refractive index            delta, Δ₀≦0.1% and an outer radius R₁ wherein R₁>4.5 μm, and        -   (ii) an outer core region 22 with an outer radius R₂ and a            minimum refractive index delta Δ₁ and alpha value α wherein            α≧5, wherein Δ₁<Δ₀, 5.5 μm≦R₂−R₁≦12 μm; and            -   an annular cladding 50 surrounding the core 20, the                cladding including        -   (i) a low index ring 53 surrounding the core and having a            minimum refractive index delta Δ_(RMIN), where Δ_(R,MIN)<Δ₁;            and        -   (ii) an outer cladding 54 with a refractive index delta            Δ_(Outer-Clad) relative to pure silica, such that            Δ_(Outer-Clad)>Δ_(R,MIN);        -   the first fiber 10 introducing a differential mode delay            DMD₁ for all wavelengths between 1525 and 1570 nm wherein 1            ps/km≦|DMD₁|≦100 ps/km, and a first differential mode delay            slope DMDS₁; and    -   (II) a second optical fiber 10′ coupled to the first optical        fiber, the second optical fiber 10′ comprising a core 20 having:        -   (i) an inner core region 21 with maximum refractive index            delta of the core, Δ₀≦0.1% wherein R₁>4.5 μm and an outer            radius R₁ wherein R₁>4.5 μm, and        -   (ii) an outer core region 22 with an outer radius R₂ and a            minimum refractive index delta Δ₁ and alpha value α wherein            α≧5, where Δ₁<Δ₀, and 5.5 μm≦R₂−R₁≦12 μm; and            -   an annular cladding 50 surrounding the core 20, the                cladding 50 including        -   (i) a low index ring 53 surrounding the core 20 and having a            minimum refractive index delta Δ_(RMIN), where Δ_(R,MIN)<Δ₁;            and        -   (ii) an outer cladding 54 with a refractive index delta            Δ_(Outer-Clad) relative to pure silica, such that            Δ_(Outer-Clad)>Δ_(R,MIN); the second fiber introducing            differential mode delay DMD₂ for all wavelengths between            1525 and 1570 nm 1 ps/km≦|DMD₂|≦100 ps/km, and a second            differential mode delay slope DMDS₂ that has an opposite            sign from the first dispersion slope DMDS₁;            and the total differential mode delay provided by the first            fiber 10 in combination with the second fiber 10′ is            DMD_(tot)=DMD₁+DMD₂, and DMD_(tot) is less than 1.0 ps/km            and more than −1.0 ps/km for all wavelengths between 1525            and 1570 nm.

According to at least some embodiments the first optical fiber 10 has aneffective area Aeff1 of LP₀₁ mode at a wavelength λ=1550 nm such that140 μm²<Aeff1_(λ=1550)<325 μm²; and the second optical fiber 10′ has aneffective area Aeff2 of LP₀₁ mode at a wavelength λ=1550 nm such that140 μm²<Aeff2_(λ=1550)<325 μm².

According to at least some embodiments,

-   -   the first optical fiber 10 comprises −0.02%≦Δ₀≦0.1%, and        −0.1%≦Δ₁≦0% where Δ₁<Δ₀; and Δ_(R,MIN)−0.25% and −0.4%        (preferably between −0.3% and −0.4%) measured relative to pure        SiO₂; and    -   the second optical fiber 10′ comprises        −0.02%≦Δ₀≦0.1%, and − and −0.1°/o≦Δ₁<0% where Δ₁<Δ₀; and        Δ_(R,MIN) between −0.25% and −0.4% (preferably between −0.3% and        -0.4%), measured relative to pure SiO₂. According to some        embodiments −0.04%≦Δ₁≦−0.004%. According to some embodiments        Δ_(Outer-Clad) is −0.2% to −0.3%.

It will be apparent to those skilled in the art that variousmodifications and variations can be made without departing from thespirit or scope of the invention. Since modifications combinations,sub-combinations and variations of the disclosed embodimentsincorporating the spirit and substance of the invention may occur topersons skilled in the art, the invention should be construed to includeeverything within the scope of the appended claims and theirequivalents.

What is claimed is:
 1. A fiber span comprising: (I) a first opticalfiber, the first optical fiber comprising a core having (i) an innercore region with maximum refractive index delta, Δ₀≦0.1% and an outerradius R₁ wherein R₁>4.5 μm, and (ii) an outer core region with an outerradius R₂ and a minimum refractive index delta Δ₁ and alpha value αwherein α≧5, wherein Δ₁<Δ₀, 5.5 μm≦R₂−R₁≦12 μm; and an annular claddingsurrounding the core, the cladding including (i) a low index ringsurrounding the core and having a minimum refractive index deltaΔ_(RMIN), where Δ_(R,MIN)<Δ₁; and (ii) an outer cladding with arefractive index delta Δ_(Outer-Clad) relative to pure silica, such thatΔ_(Outer-Clad)>Δ_(R,MIN); said first fiber introducing differential modedelay DMD₁ for wavelengths between 1525 and 1570 nm, and a firstdifferential mode delay slope DMDS₁; and (II) a second optical fibercoupled to the first optical fiber, the second optical fiber comprisinga core having: (i) an inner core region with maximum refractive indexdelta of the core, Δ₀≦0.1% wherein R₁>4.5 μm, and (ii) an outer coreregion with an outer radius R₂ and a minimum refractive index delta Δ₁and alpha value α wherein α≧5, where Δ₁<Δ₀, and 5.5 μm≦R₂−R₁≦12 μm; andan annular cladding surrounding the core, the cladding including (i) alow index ring surrounding the core and having a minimum refractiveindex delta Δ_(RMIN), where Δ_(R,MIN)≦Δ₁; and (ii) an outer claddingwith a refractive index delta Δ_(Outer-Clad) relative to pure silica,such that Δ_(Outer-Clad)>Δ_(R,MIN); said second fiber introducingdifferential mode delay DMD₂ for wavelengths between 1525 nm and 1570nm, and a second differential mode delay slope DMDS₂ that has anopposite sign from the first dispersion slope DMDS₁; and wherein totaldifferential mode delay provided by said first fiber in combination withsaid second fiber is DMD_(tot)=DMD₁+DMD₂, and DMD_(tot) is less than 1.0ps/km and more than −1.0 ps/km for all wavelengths between 1525 nm and1570 nm.
 2. The fiber span of claim 1, wherein: (i) the inner coreregion of said first optical fiber has the outer radius R₁>5 μm; and(ii) the inner core region of said second optical fiber has the outerradius R₁>5 μm.
 3. The fiber span of claim 2, wherein: (i) the innercore region of said first optical fiber has the outer radius R₁>6 μm;and (ii) the inner core region of said second optical fiber has theouter radius R₁>6 μm.
 4. The fiber span of claim 2, wherein: (i) theinner core region of said first optical fiber has the outer radius R₁>7μm; and (ii) the inner core region of said second optical fiber has theouter radius R₁>7 μm.
 5. The fiber span of claim 1, wherein said firstoptical fiber has 6 μm≦R₂−R₁≦11 μm; and said second optical fiber has 6μm≦R₂−R₁≦11 μm.
 6. The fiber span of claim 1, wherein said first opticalfiber has 8 μm≦R₂−R₁≦10 μm; and said second optical fiber has 8μm≦R₂−R₁≦10 μm.
 7. The fiber span of claim 1, wherein −0.8ps/km≦DMD_(tot)≦0.8 ps/km for all wavelengths between 1525 and 1570 nm.8. The fiber span of claim 1, wherein −0.5 ps/km≦DMD_(tot)≦0.5 ps/km forall wavelengths between 1525 and 1570 nm.
 9. The fiber span of claim 1,wherein −0.25 ps/km≦DMD_(tot)≦0.25 ps/km for all wavelengths between1525 and 1570 nm.
 10. The fiber span of claim 1, wherein −0.15ps/km≦DMD_(tot)≦0.15 ps/km for all wavelengths between 1525 and 1570 nm.11. The fiber span of claim 1, wherein DMD_(tot) is positive for atleast some of the wavelengths in the 1525 and 1570 nm range and isnegative for at least some of wavelengths in the 1525 and 1570 nm range.12. The fiber span of claim 1, wherein DMD_(tot)=0 ps/km at a wavelengthsituated between 1540 nm and 1560 nm.
 13. The fiber span of claim 1,wherein the first DMD slope is positive and the second DMD slope isnegative.
 14. The fiber span of claim 1, wherein the first DMD slope isnegative and the second DMD slope is positive.
 15. The fiber span ofclaim 1, wherein (i) 1 ps/km≦DMD₁≦100 ps/km for all wavelengths between1525 and 1570 nm and −100 ps/km≦DMD₂≦−1 ps/km for all wavelengthsbetween 1525 and 1570 nm; or (ii) −100 ps/km≦DMD₁≦−1 ps/km for allwavelengths between 1525 and 1570 nm and -1 ps/km≦DMD₁≦100 ps/km for allwavelengths between 1525 and 1570 nm.
 16. The fiber span of claim 1,wherein the first fiber has a length L₁ and the second fiber has alength L₂ and wherein 10 km≦L₁+L₂≦120 km.
 17. The fiber span of claim 1,wherein the first fiber has a length L₁ and the second fiber has alength L₂ and wherein 0.9≦L₁/L₂≦1.15.
 18. The fiber span of claim 17,wherein 0.95≦L₁/L₂≦1.1.
 19. The fiber span of claim 17, wherein 40km≦L₁+L₂≦100 km.
 20. The fiber span of claim 1, wherein the firstoptical fiber has the ratio of R₂/R₁<2.2, and the second optical fiberalso has the ratio of R₂/R₁<2.2.
 21. The fiber span of claim 1, whereinthe first optical has an effective area Aeff1_(λ=1550) of LP₀₁ mode at awavelength λ=1550 nm such that 140 μm²<Aeff_(λ=1550)<325 μm²; and thesecond optical fiber has an effective area Aeff2_(λ=1550) of LP₀₁ modeat a wavelength λ=1550 nm such that 140 μm²<Aeff_(λ=1525)<325 μm². 22.The fiber span of claim 1, wherein the first optical fiber comprises−0.02%≦Δ₀≦0.1%, and −0.05%≦Δ₁≦0%; and Δ_(R,MIN)≦−0.30%, measuredrelative to pure SiO₂; and the second optical fiber comprises−0.02%≦Δ₀≦0.1%, and −0.05%≦Δ₁≦0%; and Δ_(R,MIN)≦−0.30%, measuredrelative to pure SiO₂.
 23. A fiber span comprising: (I) a first fewmoded optical fiber, the first optical fiber comprising a core having(i) an inner core region with maximum refractive index delta, Δ₀≦0.1%and an outer radius R₁ wherein R₁>4.5 μm, and (ii) an outer core regionwith an outer radius R₂ and a minimum refractive index delta Δ₁ andalpha value α wherein α≧5, wherein Δ₁<Δ₀, 5.5 μm≦R₂−R₁≦12 μm; and anannular cladding surrounding the core, the cladding including (i) a lowindex ring surrounding the core and having a minimum refractive indexdelta Δ_(RMIN), where Δ_(R,MIN)<Δ₁; and (ii) an outer cladding with arefractive index delta Δ_(Outer-Clad) relative to pure silica, such thatΔ_(Outer-Clad)>Δ_(R,MIN); said first fiber introducing positivedifferential mode delay DMD₁ for wavelengths between 1525 nm and 1570nm, wherein 1 ps/km≦DMD₁≦100 ps/km, and a first differential mode delayslope DMDS₁; and (II) a second few moded optical fiber coupled to thefirst few moded optical fiber, the second optical fiber comprising acore having: (i) an inner core region with maximum refractive indexdelta of the core, Δ₀≦0.1% wherein R₁>4.5 μm, and (ii) an outer coreregion with an outer radius R₂ and a minimum refractive index delta Δ₁and alpha value α wherein α≧5, where Δ₁<Δ₀, and 5.5 μm≦R₂−R₁≦12 μm; andan annular cladding surrounding the core, the cladding including (i) alow index ring surrounding the core and having a minimum refractiveindex delta Δ_(RMIN), where Δ_(R,MIN)<Δ₁; and (ii) an outer claddingwith a refractive index delta Δ_(Outer-Clad) relative to pure silica,such that Δ_(Outer-Clad)>Δ_(R,MIN), said second fiber introducingnegative differential mode delay DMD₂ for wavelengths between 1525 and1570 nm wherein −100 ps/km≦DMD₂≦−1 ps/km, and a second differential modedelay slope DMDS₂ that has an opposite sign from the first dispersionslope DMDS₁; and wherein total differential mode delay provided by saidfirst fiber in combination with said second fiber isDMD_(tot)=DMD₁+DMD₂, and DMD_(tot) is less than 1.0 ps/km and more than−1.0 ps/km for all wavelengths between 1525 nm and 1570 nm.
 24. A fiberspan comprising: (I) a first few moded optical fiber, the first opticalfiber comprising a core having (i) an inner core region with maximumrefractive index delta, Δ₀≦0.1% and an outer radius R₁ wherein R₁>4.5μm, and (ii) an outer core region with an outer radius R₂ and a minimumrefractive index delta Δ₁ and alpha value α wherein α≧5, wherein Δ₁<Δ₀,5.5 μm≦R₂−R₁≦12 μm; and an annular cladding surrounding the core, thecladding including (i) a low index ring surrounding the core and havinga minimum refractive index delta Δ_(RMIN), where Δ_(R,MIN)<Δ₁; and (ii)an outer cladding with a refractive index delta Δ_(Outer-Clad) relativeto pure silica, such that Δ_(Outer-Clad)>Δ_(R,MIN); said first fiberintroducing negative differential mode delay DMD₁ for wavelengthsbetween 1525 nm and 1570 nm, wherein −100 ps/km≦DMD₁≦1 ps/km, and afirst differential mode delay slope DMDS₁; and (II) a second few modedoptical fiber coupled to the first few moded optical fiber, the secondoptical fiber comprising a core having: (i) an inner core region withmaximum refractive index delta of the core, Δ₀<0.1% wherein R₁>4.5 μm,and (ii) an outer core region with an outer radius R₂ and a minimumrefractive index delta Δ₁ and alpha value α wherein α≧5, where Δ₁<Δ₀,and 5.5 μm≦R₂−R₁≦12 μm; and an annular cladding surrounding the core,the cladding including (i) a low index ring surrounding the core andhaving a minimum refractive index delta Δ_(RMIN), where Δ_(R,MIN)<Δ₁;and (ii) an outer cladding with a refractive index delta Δ_(Outer-Clad)relative to pure silica, such that Δ_(Outer-Clad)>Δ_(R,MIN); said secondfiber introducing positive differential mode delay DMD₂ for wavelengthsbetween 1525 and 1570 nm wherein 1 ps/km≦DMD₂≦100 ps/km, and a seconddifferential mode delay slope DMDS₂ that has an opposite sign from thefirst dispersion slope DMDS₁; and wherein total differential mode delayprovided by said first fiber in combination with said second fiber isDMD_(tot)=DMD₁+DMD₂, and DMD_(tot) is less than 1.0 ps/km and more than−1.0 ps/km for all wavelengths between 1525 nm and 1570 nm.